2x+42/3x=24

Solution for 2x+42/3x=24 equation:

2x+42/3x=24

We move all terms to the left:

2x+42/3x-(24)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-24*3x+42=0

Wy multiply elements

6x^2-72x+42=0

a = 6; b = -72; c = +42;
Δ = b2-4ac
Δ = -722-4·6·42
Δ = 4176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4176}=\sqrt{144*29}=\sqrt{144}*\sqrt{29}=12\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{29}}{2*6}=\frac{72-12\sqrt{29}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{29}}{2*6}=\frac{72+12\sqrt{29}}{12}
$